why do I have no option for luxcore API
I'm running Luxrender 1.6 fine on both my Linux machine and the Windows one with LuxCore API. However, it can be tricky to set it up correctly. I can imagine two scenarios where the LuxCore API won't show up:


You have installed Luxrender correctly, but forgot to update the LuxBlend plugin. Remember that the Luxrender installer does not do this automatically for you. The Luxrender version and LuxBlend plugin really need to be of the same installer, they break compatibility very quickly.
You are trying to use the Luxrender OpenCL installer, but your system doesn't support it (that was the issue on my linux machine)


If it is 1., then you can open up Blender, go to User Preferences -> Addons, find the LuxRender plugin, and remove it completely from your system. Then, Save your User Prefs, quit Blender and restart. This ensures that when you install the new version, the Python cache will for sure be regenerated. Now install the Plugin, you can find it in the Programs folder where you installed Luxrender to. So again, User Preferences, Addons, 'Install from File', and point to your folder/Luxrender/LuxBlend.zip. It should look like this on Windows:



You should now see the addon and be able to activate it. Set the Path to your Luxrender installation correctly, Save User settings, and restart. Note from the screenshot the plugin version:



With the newest plugins, they also added a 'Update LuxBlend' button. At the moment I recommend using it, because then the 'Opactiy' option for area lights will show up, but that's a topic you can find on the LuxRender forum.

In case of 2.: Uninstall Luxrender, Download the non-open-cl package, and try that.